circle_segment_test

circle_segment_test, an Octave code which calls circle_segment(), which carries out computations associated with a circle segment, including height, width, angle, area, centroid, sampling, and quadrature.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Related Data and Programs:

circle_segment, an Octave code which carries out computations associated with a circle segment, including height, angle, area, centroid, sampling, and quadrature.

Source Code:

• circle_segment_test.m, calls all the tests.
• circle_segment_test.sh, runs all the tests.
• circle_segment_test.txt, the output file.

• circle_segment_test01.m, tests circle_segment_area_from_height().
• circle_segment_test02.m, tabulates a few quadrature rules with gqcircsegm().
• circle_segment_test03.m, plots a few quadrature rules computed by gqcircsegm().
• circle_segment_test04.m, approximates integrals with gqcircsegm().
• circle_segment_test05.m, tests circle_segment_area_from_height() and circle_segment_height_from_area().
• circle_segment_test06.m, tests circle_segment_sample_from_height().
• circle_segment_test07.m, tests circle_segment_angle_from_height() and circle_segment_height_from_angle().
• circle_segment_test08.m, tests circle_segment_contains_point().
• circle_segment_test09.m, looks at the area and centroid calculations.
• circle_segment_test10.m, checks circle_segment_test04 by calling MATLAB's QUAD2D().
• circle_segment_test11.m, demonstrates circle_segment_rotation_from_chord();
• circle_segment_test12.m, plots some rotated rules from circle_segment_rule_from_chord().
• circle_segment_test13.m, demonstrates the use of gauss() to compute some quadrature rules.
• circle_segment_test14.m, demonstrates the use of r_jacobi() to compute recursion coefficients for a quadrature rule associated with a Jacobi weight function.
• circle_segment_test15.m, demonstrates weights_t3() (and this test is NOT WORKING).
• circle_segment_test16.m, demonstrates gqcircsect().
• circle_segment_test17.m, demonstrates gqcircsegm().

Test 3 plots quadrature points for circle segments of various angles THETA:

• rule_p9_t0.392699.png, points for rule of precision 9 and THETA = pi/8.
• rule_p9_t0.785398.png, points for rule of precision 9 and THETA = pi/4.
• rule_p9_t1.5708.png, points for rule of precision 9 and THETA = pi/2.
• rule_p9_t3.14159.png, points for rule of precision 9 and THETA = pi.

Test 6 samples points from circle segments of various angles THETA:

• sample_t0.392699.png, sample for THETA = pi/8.
• sample_t0.785398.png, sample for THETA = pi/4.
• sample_t1.5708.png, sample for THETA = pi/2.
• sample_t3.14159.png, sample for THETA = pi.

Test 12 plots the quadrature points for several rules, defined on circle segments that are specified by R (circle radius), C (circle center), and P1, P2 (the points that define the chord.)

• test12_rule1.png, points for rule of radius 2, center (1,0), p1 at pi/4, p2 at 5pi/4.
• test12_rule2.png, points for rule of radius 1.5, center (-1,2), p1 at 5pi/6, p2 at 10pi/6.

Test 16 plots points for circle sectors.

• test16_acute.png,
• test16_obtuse.png,

Test 17 plots points for a circle segment.

• test17.png,